Efficient Multirate Teletraffic Loss Models Beyond ERLANG (Hardcover)

Introductions

I.1 Traffic load Definition

I.2 Traffic Congestion and GoS/QoS

I.3 System Capacity

I.4 Teletraffic Models

I.5 Traffic load Properties

I.6 Call Arrival Process

I.6.1 Superposition and Decomposition of Poisson Processes

I.6.2 Poisson Arrivals See Time Averages (PASTA)

I.7 Call Service Time

I.7.1 Markov Property

I.8 Service Systems

I.9 Little’s Law

I.10 Other Performance Metrics of Loss Systems

I.11 General Examples

I.12 Service classes – Bandwidth Sharing Policies

I.13 Classification of Teletraffic Loss Models

Part I: Teletraffic models of random input

Chapter 1 – THE ERLANG MULTIRATE LOSS MODEL

1.1 The Erlang Loss Model

1.1.1 The service system

1.1.2 Global and Local Balance

1.1.3 Call Blocking Probability

1.1.4 Other Performance Metrics

1.2 The Erlang Multirate Loss Model

1.2.1 The service system

1.2.2 The analytical model

1.3 The Erlang Multirate Loss Model under the BR policy

1.3.1 The service system

1.3.2 The analytical model

1.4 The Erlang Multirate Loss Model under the Threshold policy (EMLM/TH)

1.4.1 The service system

1.4.2 The analytical model

1.5 The Erlang Multirate Loss Model in a fixed routing network

1.5.1 The service system

1.5.2 The analytical model

1.5.3 CBP calculation by the Reduced Load Approximation method

1.6 Applications

1.6.1 The Erlang-B Formula

1.6.2 The Erlang-C Formula

1.6.3 The Kaufman-Roberts recursion

1.7 Further Reading

References

Chapter 2 – MULTIRATE RETRY – THRESHOLD LOSS MODELS

2.1 The Single Retry Model

2.1.1 The service system

2.1.2 The analytical model

2.2 The Single Retry Model under the BR policy

2.2.1 The service system

2.2.2 The analytical model

2.3 The Multi Retry Model

2.3.1 The service system

2.3.2 The analytical model

2.4 The Multi Retry Model under the BR policy

2.4.1 The service system

2.4.2 The analytical model

2.5 The Single Threshold Model

2.5.1 The service system

2.5.2 The analytical model

2.6 The Single Threshold Model under the BR policy

2.6.1 The service system

2.6.2 The analytical model

2.7 The Multi Threshold Model

2.7.1 The service system

2.7.2 The analytical model

2.8 The Multi Threshold Model under the BR policy

2.8.1 The service system

2.8.2 The analytical model

2.9 The Connection Dependent Threshold Model

2.9.1 The service system

2.9.2 The analytical model

2.10 The Connection Dependent Threshold Model under the BR policy

2.10.1 The service system

2.10.2 The analytical model

2.11 Applications

2.12 Further Reading

References

Chapter 3 – MULTIRATE ELASTIC – ADAPTIVE LOSS MODELS

3.1 The Elastic Erlang Multirate Loss Model (E-EMLM)

3.1.1 The service system

3.1.2 The analytical model

3.2 The Elastic Erlang Multirate Loss Model under the BR policy (E-EMLM/BR)

3.2.1 The service system

3.2.2 The analytical model

3.3 The Elastic Erlang Multirate Loss Model under the TH policy  (E-EMLM/TH)

3.3.1 The service system

3.3.2 The analytical model

3.4 The Elastic Adaptive Erlang Multirate Loss Model  (EA-EMLM)

3.4.1 The service system

3.4.2 The analytical model

3.5 The Elastic Adaptive Erlang Multirate Loss Model under the BR policy (EA-EMLM/BR)

3.5.1 The service system

3.5.2 The analytical model

3.6 The Elastic Adaptive Erlang Multirate Loss Model under the TH policy (EA-EMLM/TH)

3.6.1 The service system

3.6.2 The analytical model

3.7 Applications

3.8 Further Reading

References

Chapter 4 – MULTIRATE ELASTIC – ADAPTIVE RETRY LOSS MODELS

4.1 The Elastic Single-Retry Model

4.1.1 The service system

4.1.2 The analytical model

4.2 The Elastic Single-Retry Model under the BR policy

4.2.1 The service system

4.2.2 The analytical model

4.3 The Elastic Multi-Retry Model

4.3.1 The service system

4.3.2 The analytical model

4.4 The Elastic Multi-Retry Model under the BR policy

4.4.1 The service system

4.4.2 The analytical model

4.5 The Elastic Adaptive Single-Retry Model

4.5.1The service system

4.5.2 The analytical model

4.5.3 CBP, Utilization and Mean number of in-service calls

4.6 The Elastic Adaptive Single-Retry Model under the BR policy

4.6.1 The service system

4.6.2 The analytical model

4.7 The Elastic Adaptive Multi-Retry Model

4.7.1 The service system

4.7.2 The analytical model

4.8 The Elastic Adaptive Multi-Retry Model under the BR policy

4.8.1 The service system

4.8.2 The analytical model

4.9 Applications

4.10 Further Reading

References

Chapter 5 – ON-OFF MULTIRATE LOSS MODELS

5.1 The ON-OFF Multirate Loss Model

5.1.1The service system

5.1.2The analytical model

5.2 The ON-OFF Multirate Loss Model under the BR policy

5.2.1The service system

5.2.2 The analytical model

5.3 The ON-OFF Multirate Loss Model in a fixed routing network

5.3.1 The service system

5.3.2 The analytical model

5.4 Applications

5.5 Further Reading

References

Part II: Teletraffic models of quasi-random input

Chapter 6 – THE ENGSET MULTIRATE LOSS MODEL

6.1 The Engset Loss Model

6.1.1 The service system

6.1.2 The analytical model

6.2 The Engset Multirate Loss Model

6.2.1 The service system

6.2.2 The analytical model

6.3 The Engset Multirate Loss Model under the BR policy

6.3.1 The service system

6.3.2 The analytical model

6.4 The Engset Multirate Loss Model under the TH policy

6.4.1 The service system

6.4.2 The analytical model

6.5 Applications

6.6 Further Reading

References

Chapter 7 – FINITE MULTIRATE RETRY – THRESHOLD LOSS MODELS

7.1 The finite Single-Retry Model

7.1.1 The service system

7.1.2 The analytical model

7.2 The finite Single-Retry Model under the BR policy

7.2.1 The service system

7.2.2 The analytical model

7.3 The finite Multi-Retry Model

7.3.1 The service system

7.3.2 The analytical model

7.4 The finite Multi-Retry Model under the BR policy

7.4.1 The service system

7.4.2 The analytical model

7.5 The finite Single-Threshold Model

7.5.1 The service system

7.5.2 The analytical model

7.6 The finite Single-Threshold Model under the BR policy

7.6.1 The service system

7.6.2 The analytical model

7.7 The finite Multi-Threshold Model

7.7.1 The service system

7.7.2 The analytical model

7.8 The finite Multi-Threshold Model under the BR policy

7.8.1 The service system

7.8.2 The analytical model

7.9 The finite Connection Dependent Threshold Model

7.9.1 The service system

7.9.2 The analytical model

7.10 The finite Connection Dependent Threshold Model under the BR policy

7.10.1 The service system

7.10.2 The analytical model

7.11 Applications

7.12 Further Reading

References

Chapter 8 – FINITE MULTIRATE ELASTIC – ADAPTIVE LOSS MODELS

8.1 The Elastic Engset Multirate Loss Model (E-EnMLM)

8.1.1 The service system

8.1.2 The analytical model

8.2 The Elastic Engset Multirate Loss Model under the BR policy (E-EnMLM/BR)

8.2.1 The service system

8.2.2 The analytical model

8.3 The Elastic Adaptive Engset Multirate Loss Model (EA-EnMLM)

8.3.1 The service system

8.3.2 The analytical model

8.4 The Elastic Adaptive Engset Multirate Loss Model under the BR policy (EA-EnMLM/BR)

8.4.1 The service system

8.4.2 The analytical model

8.5 Applications

8.6 Further Reading

References

Chapter 9 – FINITE ON-OFF LOSS MODELS

9.1 The Finite ON-OFF Multirate Loss Model

9.1.1 The service system

9.1.2 The analytical model

9.2 Generalization of the f-ON-OFF Model to include service-classes with a mixture of finite and infinite number of sources

9.3 Applications

9.4 Further Reading

References

Part III: Teletraffic models of batched Poisson input

Chapter 10 – THE ERLANG MULTIRATE LOSS MODEL WITH BATCHED POISSON ARRIVALS

10.1 The Erlang Multirate Loss Model with Batched Poisson Arrivals

10.1.1 The service system

10.1.2 The analytical model

10.2 The Erlang Multirate Loss Model with Batched Poisson Arrivals under the BR policy

10.2.1 The service system

10.2.2 The analytical model

10.3 The Erlang Multirate Loss Model with Batched Poisson Arrivals under the Threshold policy

10.3.1 The service system

10.3.2 The analytical model

10.4 Applications

10.5 Further Reading

References

Chapter 11 – BATCHED POISSON MULTIRATE ELASTIC – ADAPTIVE LOSS MODELS

11.1 The Elastic Erlang Multirate Loss Model with Batched Poisson Arrivals (BP-E-EMLM)

11.1.1 The service system

11.1.2 The analytical model

11.2 The Elastic Erlang Multirate Loss Model with Batched Poisson Arrivals under the BR policy (BP-E-EMLM/BR)

11.2.1The service system

11.2.2 The analytical model

11.3 The Elastic Adaptive Erlang Multirate Loss Model with Batched Poisson Arrivals (BP-EA-EMLM)

11.3.1 The service system

11.3.2 The analytical model

11.4 The Elastic Adaptive Erlang Multirate Loss Model with Batched Poisson Arrivals under the BR policy (BP-EA-EMLM/BR)

11.4.1 The service system

11.4.2 The analytical model

11.5 Applications

11.6 Further Reading

References